\[ y'(x) \left (6 y(x)^2-\frac {2 y(x) f'(x)}{f(x)}\right )+f(x) y(x)+g(x) y(x)^2+4 y(x) y''(x)-2 y(x)^2 y'(x)-3 y'(x)^2+y(x)^4=0 \] ✗ Mathematica : cpu = 0.707854 (sec), leaf count = 0 , could not solve
DSolve[f[x]*y[x] + g[x]*y[x]^2 + y[x]^4 - 2*y[x]^2*Derivative[1][y][x] + (6*y[x]^2 - (2*y[x]*Derivative[1][f][x])/f[x])*Derivative[1][y][x] - 3*Derivative[1][y][x]^2 + 4*y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+(6*y(x)^2-2*diff(f(x),x)*y(x)/f(x))*diff(y(x),x)+y(x)^4-2*y(x)^2*diff(y(x),x)+g(x)*y(x)^2+f(x)*y(x)=0,y(x))